SuperSpec is a novel on-chip spectrometer we are developing for multi-object, moderate resolution (R = 100 - 500), large bandwidth (~1.65:1) submillimeter and millimeter survey spectroscopy of high-redshift galaxies. The spectrometer employs a filter bank architecture, and consists of a series of half-wave resonators formed by lithographically-patterned superconducting transmission lines. The signal power admitted by each resonator is detected by a lumped element titanium nitride (TiN) kinetic inductance detector (KID) operating at 100-200 MHz. We have tested a new prototype device that is more sensitive than previous devices, and easier to fabricate. We present a characterization of a representative R=282 channel at f = 236 GHz, including measurements of the spectrometer detection efficiency, the detector responsivity over a large range of optical loading, and the full system optical efficiency. We outline future improvements to the current system that we expect will enable construction of a photon-noise-limited R=100 filter bank, appropriate for a line intensity mapping experiment targeting the [CII] 158 micron transition during the Epoch of Reionization